The best shorts that have worked for me and don't cause this issue have been the PI Symphony and Gore Oxygen. The Gore chamois(s) is the best I've found (I like the chamois in the Oxygen as well as the one in the cheaper Power models), so I'm pretty much sold on sticking with that brand.

I tried a few shorts without grippers and liked the shorts' fit and found them flattering, but never found one with a chamois that worked for me.